Master of Science
Accurate structure analysis of high-resolution 3D biomedical images of vessels is a challenging issue and in demand for medical diagnosis nowadays. Previous curvature regularization based methods [10, 31] give promising results. However, their mathematical models are not designed for bifurcations and generate significant artifacts in such areas. To address the issue, we propose a new geometric regularization principle for reconstructing vector fields based on prior knowledge about their divergence. In our work, we focus on vector fields modeling blood flow pattern that should be divergent in arteries and convergent in veins. We show that this previously ignored regularization constraint can significantly improve the quality of vessel tree reconstruction particularly around bifurcations where non-zero divergence is concentrated. Our divergence prior is critical for resolving (binary) sign ambiguity in flow orientations produced by standard vessel filters, e:g: Frangi. Our vessel tree centerline reconstruction combines divergence constraints with robust curvature regularization. Our unsupervised method can reconstruct complete vessel trees with near-capillary details on both synthetic and real 3D volumes. Also, our method reduces angular reconstruction errors at bifurcations by a factor of two.
Zhang, Zhongwen, "Vessel Tree Reconstruction with Divergence Prior" (2019). Electronic Thesis and Dissertation Repository. 6008.
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